Y=x^2+15x+50

Solution for Y=x^2+15x+50 equation:

=Y^2+15Y+50

We move all terms to the left:

-(Y^2+15Y+50)=0

We get rid of parentheses

-Y^2-15Y-50=0

We add all the numbers together, and all the variables

-1Y^2-15Y-50=0

a = -1; b = -15; c = -50;
Δ = b2-4ac
Δ = -152-4·(-1)·(-50)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*-1}=\frac{10}{-2}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*-1}=\frac{20}{-2}
=-10
$